ar X iv : h ep - p h / 98 02 41 5 v 1 2 5 Fe b 19 98 INFLATION

The shortcomings of the Standard Big Bang Cosmological Model as well as their resolution in the context of inflationary cosmology are discussed. The inflationary scenario and the subsequent oscillation and decay of the inflaton field are then studied in some detail. The density perturbations produced during inflation and their evolution during the matter dominated era are presented. The temperature fluctuations of the cosmic background radiation are summarized. The non-supersymmetric as well as the supersymmetric hybrid inflationary model is introduced and the 'reheating' of the universe is analyzed in the context of the latter and a left-right symmetric gauge group. The scenario of baryogenesis via a primordial leptogenesis is considered in some detail. It is, finally, pointed out that, in the context of a supersymmetric model based on a left-right symmetric gauge group, hybrid inflation, baryogenesis via primordial leptogenesis and neu-trino oscillations are linked. This scheme, supplemented by a familiar ansatz for the neutrino Dirac masses and mixing of the two heaviest families and with the MSW resolution of the solar neutrino puzzle, implies that 1 eV < ∼ mν τ < ∼ 9 eV. The mixing angle θµτ is predicted to lie in a narrow range which will be partially tested by the Chorus/Nomad experiment. The Standard Big Bang (SBB) Cosmological Model 1 has been very successful in explaining, among other things, the Hubble expansion of the universe, the existence of the Cosmic Background Radiation (CBR) and the abundances of the light elements which were formed during primordial nucleosynthesis. Despite its great successes, this model had a number of long-standing shortcomings which we will now summarize: 1.1 Horizon Problem The CBR, which we receive now, was emitted at the time of 'decoupling' of matter and radiation (which essentially coincides with the time of recombina-tion of atoms) when the cosmic temperature was T d ≈ 3, 000 K. The decoupling time, t d , can be calculated from T 0 T d = 2.73 K 3, 000 K = a(t d) a(t 0) = t d t 0 2/3 , (1) where t 0 , T 0 are the present cosmic time and temperature of CBR and a(t) is the dimensionless scale factor of the universe at cosmic time t normalized 1